Some streams of literature do require not only cardinal utility but also interpersonal utility comparisons. For example, the Bergson-Samuelson social welfare function is based on utilities of individuals that are comparable [1]}. Likewise, auction theory and large parts of the mechanism design literature assume vNM utility functions and interpersonal utility comparisons. These strong assumptions allow for landmark results such as the dominant-strategy incentive-compatible Vickrey-Clarke-Groves mechanism [2]}. Notably, the Bayes-Nash equilibrium (a generalization of NE for games with incomplete information) provides a solution concept for finding equilibrium in mechanisms without dominant strategies.
For many applications such as spectrum sales or electricity markets, cardinal utilities, and even interpersonal (or inter-firm) utility, comparisons in money might be adequate. However, for others, they are too much to ask for.
